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AIP conference proceedings

Single-Photon Two-Qubit Logic Gates

Marco Fiorentino B

Published Jan 1, 2004• 1 citation
Publisher

Abstract

We present experimental results of deterministic linear optical Controlled‐NOT and SWAP gates for single‐photon two‐qubit quantum logic. In our implementation one qubit is encoded in the polarization degree of freedom of the photon and the other is encoded in the momentum. Momentum‐ and polarization‐controlled NOT gates are demonstrated. They are then combined to form a SWAP gate to convert pairs of momentum‐entangled photons into polarization‐entangled photons.

DOI
10.1063/1.1834418

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We present experimental results of deterministic linear optical Controlled‐NOT and SWAP gates for single‐photon two‐qubit quantum logic. In our implementation one qubit is encoded in the polarization degree of freedom of the photon and the other is encoded in the momentum. Momentum‐ and polarization‐controlled NOT gates are demonstrated. They are then combined to form a SWAP gate to convert pairs of momentum‐entangled photons into polarization‐entangled photons.
A SWAP operation between different types of qubits of single photons is essential for manipulating hyperentangled photons for a variety of applications. We have implemented an efficient SWAP gate for the momentum and polarization degrees of freedom of a single photon. The SWAP gate was utilized in a single-photon two-qubit quantum logic circuit to deterministically transfer momentum entanglement between a pair of down-converted photons to polarization entanglement. The polarization entanglement thus obtained violates Bell's inequality by more than 150 standard deviations.
We demonstrate a robust implementation of a deterministic linear-optical controlled-not gate for single-photon two-qubit quantum logic. A polarization Sagnac interferometer with an embedded 45 degrees -oriented dove prism is used to enable the polarization control qubit to act on the momentum (spatial) target qubit of the same photon. The optical controlled-not gate requires no active stabilization because the two spatial modes share a common path, and it is used to entangle the polarization and momentum qubits.
We present a general scheme for a family of linear-optical quantum control gates, including controlled-not and controlled-swap gates for two or three qubits. Our approach utilizes polarization-path-entangled pairs of photons and encodes qubits in mixed degrees of freedom with the control qubit specifically occupying the polarization degree of freedom. By exploiting multiple degrees of freedom and initial state entanglement of the two photons, the proposed control gates do not require any ancilla photons or measurement-induced nonlinearities. Since our gates are purely linear and we implicitly use nonlinearities in a standard manner to create entanglement via parametric nonlinear process, our work demonstrates that a need to have nonlinearities in the photonic gates can be shifted to the state preparation stage; the cost of such shift is that the construction of a certain class of single-qubit operations, such as Hadamard, needs to be probabilistic. In particular, we focus on a deterministic linear-optical quantum Fredkin (controlled-swap) gate and perform a full characterization of the gate performance with a high fidelity typically well above 9999%99 under realistic conditions. The proposed control gates rely on simple linear-optical elements and polarization-entangled photon pairs readily generated from ubiquitous sources, making the gates experimentally feasible with current technologies.
The information-carrying capacity of a single photon can be vastly expanded by exploiting its multiple degrees of freedom: spatial, temporal, and polarization. Although multiple qubits can be encoded per photon, to date only two-qubit single-photon quantum operations have been realized. Here, we report an experimental demonstration of three-qubit single-photon, linear, deterministic quantum gates that exploit photon polarization and the two-dimensional spatial-parity-symmetry of the transverse single-photon field. These gates are implemented using a polarization-sensitive spatial light modulator that provides a robust, non-interferometric, versatile platform for implementing controlled unitary gates. Polarization here represents the control qubit for either separable or entangling unitary operations on the two spatial-parity target qubits. Such gates help generate maximally entangled three-qubit Greenberger-Horne-Zeilinger and W states, which is confirmed by tomographical reconstruction of single-photon density matrices. This strategy provides access to a wide range of three-qubit states and operations for use in few-qubit quantum information processing protocols.Photons are essential for quantum information processing, but to date only two-qubit single-photon operations have been realized. Here the authors demonstrate experimentally a three-qubit single-photon linear deterministic quantum gate by exploiting polarization along with spatial-parity symmetry.